R. R. IRANI A N D C. F. CALLIS
1398
Vol. 64
lined by Amdur and Mason. 2o At most , the thermal diffusion contribution to VH*O was about 10%. Thus, while the effect is not always as small as one v,E - 5 & I.!!?] would like, the error caused by its neglect is a t (B1) X* 1' dz worst probably no larger than others, and the where the F ositive sign holds if the trace i is heavier simplification this neglect brings to an already comthan the II sin component, and the negative sign plex analysis is most welcome. if the trace is lighter. k~ is the thermal diffusion C. Pure Oxygen Approximation for Thermal ratio given by Conductivity.-The use of XO, instead of the true mixture thermal conductivity was occasioned kT S zk D,T/NIM,D, (B2) primarily (as with the other approximations) by DIT being the trace thermal diffusion coefficient, the great simplification it afforded. The actual and N the total molar density. In most cases, flame mixture was composed throughout of roughly DiT itself is positive if the trace is heavier and nega- 80% oxygen, with the remaining 20% mostly lighter tive if it is lighter than (in our case) oxygen, so components (except for COZ) which might be exthat k T is generally positive. Therefore, the pected to increase the thermal conductivity over common situation is for a heavier trace species to that of pure oxygen. To get some idea of the error thermally diffuse upstream and a lighter species introduced here, an approximate ca1culation2l downstream. was made of X for a mixture composed of 85% The thermal diffusion correction to the diffusion oxygen and 15% water a t 1500'K. This gave a velocity was carried out for the case of HzO, for value about 15% higher than the pure oxygen value. which it probably would be as large as for any of Such an increase in X would improve the enthalpy the major species. The necessary thermal dif- balance of Fig. 9 somewhat, fusion data were computed from our concentra(20) I. Amdur a n d E. A. Mason. P h y s F l u i d s , 1, ,370 (1958). tion diffusion coefficients and viscosities as out(21) R. S.Brokaw, J . Chem Phya., 29, 391 (14581. velocity including thermal diffusion may be written lo
[z
METAL COMPLEXING BY PHOSPHORUS CORIPOUNDS. I. THE THERMODYNAMICS OF ASSOCIATION OF LINEAR POLYPHOSPHATES WITH CALCIUM' BY R. R. IRAXI AND C. F. CALLIS Research Department, Inorganic Chemicals Division, Monsanto Chemical Company, St. Louis 66, Missotcri Received February 19, 1960
The stabilities of calcium complexes of the linear chain phosphates have been evaluated, from nephelometric titrations in the presence of an added precipitating agent, as a function of pH, temperature, ionic strength and length of the phosphate chain. At high pH values the number of phosphorus atoms that are in equilibrium with one calcium ion was evaluated and found to be 2, 3, 4,4 and 5 for linear phosphates with average chain lengths of 2, 3, 6, 14 and 60, respectively. The free energy change a t 25' accompanying the association of calcium with P z O T - ~HPzOT-~, , PgOla-5,HP301a-4 and HzP301p-a was found to be -7.6, -4.9, -9.5, -5.3 and -5.3 kcal., respectively. For the longer chain phosphates the corresponding free energy changes were found to be -10.2 f 0.2 kcal. and independent of chain length. For C a P 3 0 1 ~ -and 3 CaP20T-2 the enthalpies of association were found to be -3.2 and 4.6 kcal., respectively, whereas for the long chain phosphates the values were negligibly small. A large positive entropy change (21-46 e.u.) was found to accompany association in all cases. This positive entropy change is attibuted to the release of waters of hydration upon association. The frer energy, enthalpy and entropy of formation of aqueous pyrophosphate and tripolyphosphate anions are evaluated from published data.
Introduction (1) to check and extend by an indepcndent method The ability of the polyphosphates to form soluble the results of Watters, et al.,2 and thereby test the complexes with calcium ions has been known for validity of both methods; ( 2 ) to investigate the about a century. Several investigators have re- effects of pH, total ionic strength and temperaported evaluation of complexity constants. How- ture on the stability constants in order to evaluate ever, as indicated by Watters, et aLlZmost of the the thermodynamic formation constants and the evaluations were carried out in the presence of related free energies, enthalpies and entropies of alkali metal ions that are well known to form com- complex formation; (3) to investigate the effect of plexes of their own with the polyph~sphates.~the chain length of the polyphosphates on the stah review4 on this subject appeared as recently as bility of their calcium complexes: and (4)to use the resulting thermodynamic quantities to te3t 1958. The purpose of this study is fourfold, namely recent proposed theories5-' 011 entropy changeq 7 accompanying association reactions in solution. (1) Prvsented before t h e Division of Inorganic Chemistry, 137th meeting .,f t h e American Chemical Society, Cleveland, Ohio, April, 1960. (2) J. 1. Watters a n d 8. M. Lambert, J . Am. Chem. Soc., 81, 3201 (1959). (3) U. P. Strauss a n d P. D. Ross, ibid., 81, 5295 (1959). (4) J. R. Van U'azer and C. F. Callis, Chem. Reus., 68, 1011 (1958).
(5) E. L. King, J . Chem. Educ., 30, 71 (1953). ( G ) J. W.Cobble, J . Chem. Phys., 21, 1446 (1953). (7) W. J. Hamer, "The Structure of Electrolytic Solutions," J o h n Wiley and Sons, Inc., New York, N. Y., 1959, Chapter 2 4 by J. & I , Austin, R. A. Matheson and H. N. Parton.
Oct., 1960
METALCOMPLEXING BY PHOSPHORUS COMPOUNDS
1399
Experimental Chemicals.-Sodium tripolyphosphate hexahydrate was used aa the source of tripolyphosphate ions. It was prepared by four repeated fractional crystallizations of commercial tripoly hosphate from aqueous solutions of ethyl alcohol. The E a 1 sample showed analysis to better than 99.7% Na6P$O10,exh.ibiting the proper Na2O/PzO6ratio.s.9 Mallinckroclt analytical reagent grade tetraaodium pyrophosphate decahyclrate was used as the source of pyrophosphate anions and gave analysis to better than 99.5% NadPI07, exhibiting the proper Na20/PZO6ratio.9 The three anhydrous long chain sodium polyphosphates that were investigated were randomly reorganized products, identified only by their NazO/Pz06 ratios.lO The molar NazO,(P%O6 ratios were found to be11 1.34, 1.15 and 1.033, indicating a dlstribution of chain lengths having an averagelo of 6, 14 and 60 phosphorus atoms per molecule, respectively. Reagent grades of tetramethylammonium and tetraethylammonium bromides, chlorides and hydroxides were purchased from Eastman Kodak Co. All the tetramethylammonium polyphosphates were prepared by ion exchanging the sodium salts with the hydrogen form of 100-200 mesh Dowex 50W-X2 and neutralizing the resulting aeids immediately with tetramethylammonium hydroxide, 2s previously described.12 The stock solutions were maintained a t 25" and a pH of 12 to avoid hydrolytic degradation. The final phosphorus content of the stock solutions was checked13 against the make-up concentrations and these values agreed within experimental error. The different stock solutions were found t o contain 0.015-0.023 mole of phosphorus per 100 ml. The tetramethylammonium iodate was prepared by neutralizing Fkher reagent grade iodic acid with tetramethylammonium hydro ride. The other chemicals were C.P. grade. Equipment .-The nephelometric titrations were performed by recording the light transmittance of a solution containing the polyphosphate and precipitating anion as the calcium titrant was added in increments t o an unstirred solution, followed by agitation. This cycle was repeated until the end-point was passed, as evidenced by persistence of a precipitate. The housing and sensing elements of a Sargent-Malmstadt photometric titratcir14 were the basic elements in the set-up. The voltage output of the photoelectric cell was stepped down through a 0.5 megohm helipot and fed into a 0-100 MV Brown recorder with a 1sec. response. The chart speed was usually 1 in./min. A 25-ml. automatic buret was fastened over the titrator and the input of a solenoid valve that regulates flow of titrant was hooked into one of the leads of a Flex-Pulse relay-timer, manufactured by Eagle Signal Corp., Moline, Ill. The other lead of the relay-timer was attached to the input of a 2000 r.p.m. stirring motor. The stirring cyclz of the timer was 2 min., whereas the additionof-titrant ((>a++solution in this case) cycle varied from experiment to experiment, but ranged from 2-10 seconds. Capillary delivery tips of various diameters were inserted between the buret and the photometric titrator to further control the rate of titrant delivery. After repeated experimentation ix was found that single titrant shots that were delivered by the above described process (0.15-0.9 cc.) did not vary by more than 0.02 cc., provided only the top 7 cc. of the buret was used, and this maximum volume never was exceeded. When more than 7 cc. was required, the titration was stopped and the buret refilled. Procedure.-Aliquot volumes of the polyphosphate stock solution and the calcium-precipitating anion solution (either oxalic acid or tetramethylammonium iodate) were pipetted into a 400-m1. beaker, containing 150 ml. of distilled water. (8) 0. Quiniby, T H I S JOURNAL, 58, 603 (1954). (9) J. R. Van Wazer, "Phosphorus and Its Compounds," Vol.
I,
Interscience Publ. Co., New York. N. Y.,1958. (10) Ref. 9, Chapter 12. ( 1 1 ) Kindly determmed by Mr. -4. B. Finley of Monsanto's Columbia, Tennessee plant. (12) J. R. Van Wazer, E. J. Griffith and J . F. McCullougb, J . Am. Chem. Soe., 77, 287 (1955). (13) J. R. Van Waser. E. J. GriRth and J. F. McCullougb, Anal. Chsm., 26, 1755 (19541. (14) E.H.Emrwnt C o . , Chicago, "Scientlfio hlethods," Vol. 10, No. 2. Sect. 1, 1953
I
1
7
6 5 4 3 2 1 No. of titrant shots. recorder chart during nephelometric titration.
Fig. 1.-Typical
h
L
I I
\ \ I
,
l
,
l
,
l
,
l
,
l
,
l
,
l
,
4 6 8 10 12 14 16 No. of titrant shots. Fig. 2.-Typical~determination~of end-point. 2
The pH of the solution was adjusted to the desired value through the addition of either aqueous HC1 or aqueous tetramethylammonium hydroxide. Additional water was put in so that the total solution volume was 250 cc. An appropriate weight of tetramethylammonium bromide15 then waa dissolved to give the desired ionic strength, namely, 0.1, 0.5 or 1.0. The pH was again checked at this point and was never found to have changed. It was assumed that the added tetramethylammonium bromide was completely ionized, and since only a small fraction of the ionic strength was due to the other cations and anions, the assumption of total ionization of the other salts is not important. The beaker containing the solution then was placed in the titrator and the recorder and relay-timer switches were initiated. The shots of titrant solution were added periodically when the stirrer was off, causing high localized calcium ion concentrations that precipitated CaCzO4: If more than 2 min. of stirring were required for equilibration, smaller titrant shots were used. When the stirring cycles started, the precipitate dissolved in the excess polyphosphate. The cycles were automatically repeated until permanent and noticeable turbidity resulted which did not disappear upon more stirring. The total titrant volume and the number of shots then were read, and the volume per shot noted. Meanwhile, the p H of the solution was controlled by periodic additions of tetramethylammonium hydroxide; this was not necessary for pol hosphate solutions with a pH over 10.5 due to buffering. %he molarity of the calcium nitrate solutions was either 4.43 X or 8.86 X 10-2 (from the solution make-up with Ca(N0&4H~O)andchecked t o within 0.1yo with disodium ethylenediaminetetraacetate titrations a t a p H of 13 in the presence of calcon indica(15) When tetramethylammonium chloride was used instead of the bromide, the same results were obtained, brit the system came t o equilibrium more slowly. Therefore, the bromide a-as used exclusively in all the experiments described here.
R. R. IRANIAND C.F. CALLIS
1400
tor 16 A +esh calcium solution was prepared every week, during which period no evidence of carbonate contamination was found. Figure i is a reproduction of a typical recorder chart containing the continuous record of changes in the light intensity of 550 mp filtered light across the beaker during a titration. The transmitted light intensities at the end of each cycle, the I , values in Fig. 1, were plotted us. the number of shots. I'sually two intersecting lines resulted as illustrated in Fig. 2 The point of intersection of these two lines was taken as the point of incipient precipitation. The product of the nlimber of shots a t that point times the volume/shot is the total volume of calcium solution that can be held by the poly1)hosphates prior to calcium precipitation under the specific ronditione . To prove that the above described procedure did give cquilibriuin valuw, the equilibrium was approached many times from both rides. First, six t o seven solutions with controlled alkaline p € values I having various amounts of calcium brit the same amounts of polyphosphate and precipitating mion were prepared and stirred with a magnetic stirrer for 1-2 weeks. In this time period no hydrolytic degradation is pxpected.12 The end-point was then determined from light intensity measurements. Some mixtures originally clear b c a m e turbid with time. This supersaturation'' is a wrious source of error if sufficient equilibration time is not allowed and this probably accounts for some of the discrepancies found in the literature. In the second procedure, excess calcium was added t o form a precipitate. Various amounts of polyphosphate then were added and the solutions were stirred for one week. The endpoint was again noted from light intensity measurements. In both procedures the results agreed within experimental error (0.2 cc.) with those from the rapid semi-automatic titration method developed and used in this work. Since the semi-automatic titrations were performed in an airconditioned laboratorv ( 2 5 " ) where temperature fluctuations are less than rt0.2" for an experiment duration, no special temperature control was used for the 25" runs. For the 37 and 50" experiments, the temperature was controlled to within rt0.2' by heating the solutions 2-3 times during titration. The ri3peatability of the results was not different a t the thrtae temperatures, and was found to be =!=O 1 cc.
Vol. 64
respectively. Our data agreed well with those available in the literature20 when compared under the same conditions. The plot of log solubility us. 1/T gave straight lines a t the different ionic strengths, and the lines were parallel. From our measurements described above and from those of others a t 37'" and different pH values, it is concluded that the solubility product of CaC204.H20does not change with pH in the neutral or alkaline region. Also, changes in the solubility product of CaC20, due t o the addition of foreign ions other than C a + + or GO4- are only dependent upon changes in the total ionic strength.
Equilibria and Treatment of Data General.-The polyphosphates can be considered to be typical polyelectrolyteszi consisting of a chain of alternate phosphorus and oxygeii atoms that are held together by predominantly covalent bonding. Evidence for more than just simple electrostatic attraction holding the polyphosphate anions close to the "complexed" cations has been advanced and, hence, the sequestration data will be interpreted along the lines of "specific site binding."22 In general, the association reaction between a cation and a polyphosphate anion can be represented by equation (l), omitting the charges on the ions bf.(H,O)a
+ p's(e).(Ir,o)b=
+ +
~ I [ S ( ~ ) I ~ . ( E I ~(Oa ) ~ ZI
- C)II?O
(1)
where a, b and c are hydration numbers, 0 is the number of phosphorus atoms per site, S , and P is the number of sites occupied by one cation. S may or may not have one or more hydrogens attached. The idea that linear polyelectrolytes are composed of individually independent sites has been suggested by Flory,*3who envisioned the sites or segments as having elastic membranes separatPrecipitates and Solubility Products ing them. The numerical values of P , b, c and 0 The unwashed precipitates formed a t the end of the nephel- presumably are dependent upon the chain length ometric calcium titrations of oxalate-polyphosphate solu- and hydrogen form of the polyphosphate, and may tions were unequivocally proven t o be CaC204.H20 from (1) X-ray measurements that showed an identical diffraction have different values for the same chain length pattern to C.P. CaC204.H20, (2) wet chemical analyses for molecule, being distributed around a certain mean CaO11 and oxalate, and (3) the fact that the PzOS contents of value. the unwashed precipitates were less than 2% in all cases, the For each specific binding phenomenon, we may order of magnitii de for adsorption. Washing the precipitate twice brought the PZOScontent down to 0.1-0.2%,while the define a binding constant3 CaO/oxalnte ratio did not change. The solubility product of CaC204at the desired conditions was evaluated as follows. Half a gram of freshly prepared CaC204.Hz0 was shaken mechanically for several days a t the desired temperature with 500 ml. of aqueous solutions made up to ionic strengths of 0.1 or 1.0 using tetramethylammonium hydroxide. The resulting saturated solutions were titrated with a 0.1 N KMn04 solution standardized with predried Na2C204. The solubility product of CaC204a t 25" was found to be 1.32 X 10-8 a t 0.1 ionic strength; literature values a t the same temperature and ionic strength are 1.26 X 10-8 and 1.96 x 10-8 in aqueous solutions of N a C P and NH4C1,'g respectively. The value at unit ionic strength and 25' was in good agreement with literameasured t o be 7.80 X ture values of 7.29 X 10-8 and 8.75 X 10-8 in aqueous solutions of NaC1'8 and "4x0s,l9 respectively. Similarly, the solubility produrt of CaC204 a t 37" was measured and found to be 2.43 X 10-8 and 1.29 X 10-7 a t ionic strengths of 0.1 and 1.0, respectively. A t 50", it was found t o be 4.32 x 10-8 and 2.45 X 10-7 at ionic strengths of 0.1 and 1.0,
-
(16) C. A . Goetz and R. C. Smith, Iowa State J . Sei., 34, No. 1, 81 (195Q).
(17) C. I. Mehltrettcr, B. H. Alexander and C. E. Rist, Ind. En& Chem., 45, 2782 (1q53). (18) W. I 1 XlcCcmas and W. Kioman, J . A m . Cbsm. SOC.,64, 2946 (1942) JOURNAL, 44, 1fiG (1940). (IO) If C l i r t l \ n Ctnd I?. €3. Pall, THIS
I n the special case of nephelometric titrations, if an end-point is chosen so that crystalline CaBd just starts precipitating, then in addition to equation 2 ICep= [Ca++][B-2'd]d (3 1 where K,, is the solubility product of CaBd, and d can have the values of either one (divalent precipitating anion) or two (monovalent precipitating anion). Pyrophosphate or Tripolyphosphate.-For t,he or tripolyphosphate well-defined pyrophosphate __ anions, not more than two hydrogen- forms are needed to fit acid-base titration data. Therefore, (20) W. F. Linke. "Solubilities," D. Van Nostrand Co., Inc., New York, N. Y.. 1958, 4th Ed.,Vol. I. (21) C. F. Callis, J. R. Van Wazcr and P. G . .4rvan, Chem. Rrvs., 64, 777 (1954). ( 2 2 ) U. P. Strauss, D. Woodside and P. Winernan, THIBJOURNAL. 61, 1353 (1957). (23) P. J. Flory, "Prinriples of Polymer Chemistry." Cornel1 University Press, Tthaca, N. Y . , 1953, r,. CRO.
Oct., IOGO
at any pII, three equations are sufficient to define the calcium-hydrogen-phosphate interaction, in the absence of other phosphate-complexing cations
(5)
where the subsc-ipt h designates a site containing an additional hydrogen. Average values of each of the parameters 8, P , Ph were computed from the experimental data as follows: ,lrbitrary values of P were first assigned, and then ca. 10 values of 8 were computed by equating pairs of the expression for the apparent dissociation constant, each from a different experiment a1 measurement. The best fit for various combinatioiis of P and 8 was judged from the constancy of the dissociation constant for the entire set of experiments. -4s shown in the Results and Discussion section, the best fit to the experimental data for either pyrophosphate or tripolyphosphate was found for
s(e, = sl,(e)
(6)
P=Ph=1
(7)
Inchiding the restrictions in equations 6 and 7, the material balnnces for ralcium and phosphorus nt the point of illi7ipient precipitation are yz = [ C a t + ]
A
_ I O L_ = e
1301
hIJZTAL COhIPLEXING BY h-IOSPlIORUS COMPOUNDS
+ [CnS(e)]+ [CaHS(e)]
[swi + [ I [ s ( ~ + ) I I ( c ~ s (+~[caHS(e)! )I
(8) (9)
where 1OL/8 is the molarity of sites, A the total volume of the solution in cc., and y is the number of cc. of a calcium solution of 2 molarity. The initial concentration of phosphates is L moles of phosphorus ptlr LOO ml., and the concentration of the “I3 salt” (e.g., tetramethylammonium oxalate) is s g./100 ml. In addition, the solubility product Ksr,is related to the free calcium ion concentration and the moleciilzr weight of the “B salt,” AT,, by thc c>xprrwioir Cu++ = K,,
(:gi)d
where d is the same integer in equation 3. The [Ca++]term in equation 8 is negligible compared to the other two terms, as will be seen from the magnitudezi of PCaSce! and Pc~Hs(o). If cqnat,ior!s 5 , 8 a d 0 are com!mied then
AI
Ksp
[?\I’ - y]
(k)Bcas(e)[If (H+)/pr~s(e)](13)
If 8, liep and PHS(O)are known, then plots of the left-hand side of equation 15 2’s. sd at suitable pIf values should give a straight line whose slope can be used to compute both PcSs(e) and PCaHS(8). Whe11PC~HS(O) >> pcas(~),and the p H is such that (H+)/@r
